Questions tagged [qutrit]

For questions related to quantum trits i.e. three-level (dimensional) quantum mechanical systems. They are higher dimensional analogues of qubits (aka quantum bits), which are two-level (dimensional) quantum mechanical systems.

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How to write the three-qubit GHZ state in the Pauli basis?

How can one write the GHZ state defined in Ket notation as $|\psi\rangle= \frac{1}{\sqrt{2}} \left(|000\rangle + |111\rangle\right)$, in terms of Pauli matrices $\sigma_{1},\sigma_{2},\sigma_{3}$?
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Can we rotate Bloch vectors for qudits like we do with qubits in the Bloch sphere?

I have been looking into the Bloch vectors for qudits and have been wondering if we can do rotations that are similar to the rotations in the qubit Bloch sphere. Like, once we create a Bloch vector ...
6
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1answer
168 views

What is the set of generators for the qutrit Clifford group?

According to this article, any Clifford gate, acting on $n$ qubits, can be generated by Hadamard, CNOT, and S gates. What are the set of generators for qutrit Cliffords?
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Can a triplet be a qutrit?

Original question A triplet is a space that consist of three states that have the same total angular momentum (spin 1). If we restrict ourselves to a set of quantum gates that keep triplet states in ...
4
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1answer
145 views

Qutrit analogues of controlled Z and cc-Z gates

I am trying to look for the qutrit analogues of a controlled-Z, and a cc-Z (Z gate with two controls) for qubits. There is a previous answer that gives a qutrit analogue of a CNOT gate, but does not ...
4
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1answer
101 views

Cliffordness of the qutrit Hadamard gate

Consider a simple generalization of the Hadamard gate to qutrits, defined as follows. \begin{equation} \begin{pmatrix} \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0\\ \frac{1}{\sqrt{2}} &...
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0answers
50 views

Can someone elaborate how to use Qutrits to do teleportation? And the unitary operation Bob needs to do? [duplicate]

I can understand doing teleportation by using qubits, however, I am stuck there when it comes to qutrits and the operation Bob needs to perform. Suppose Alice and Bob are sharing the most entangled ...
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2answers
106 views

Is there a quantum processor with physically implemented Toffoli gate?

Recently, I came across the article Realization of efficient quantum gates with a superconducting qubit-qutrit circuit where its authors proposed a physical implementation of three qubits quantum ...
3
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1answer
130 views

Can a single qutrit in superposition be considered entangled?

Often in quantum computing the idea of quantum superposition is introduced well before the concept of entanglement. I suspect this may be because our conception of (classical) computing privileges ...
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1answer
48 views

How do we restrict to a limited number of dimensions, say 3 for qutrits, while using OAM states of light?

When a azimuthal phase $\mathrm{e}^{il\phi}$ is applied to gaussian beams having plane wavefront, they develop a corkscrew sort of structure and therefore possess an orbital angular momentum in ...
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1answer
116 views

Color-Space as Effective and Intuitive Qutrit Physical Realization? [closed]

Has anyone used or considered color-space and color superposition for Qutrit work? A classical color-sphere has black and white at its poles, a grey scale as its axis, pure spectral colors as a color-...
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1answer
578 views

Defining standard qubit gates for qutrits

I am actually working on quantum computing with qutrits. I am trying to define standard qubit gates for qutrits. The CNOT gate for qubits is defined as follows: $$|x,y\rangle \to |x,y+x \bmod 2\rangle....
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What proportions of certain sets of PPT-two-retrit states are bound entangled or separable?

For two particular (twelve-and thirteen-dimensional) sets of two-retrit states (corresponding to 9 x 9 density matrices with real off-diagonal entries), I have been able to calculate the Hilbert-...
3
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1answer
95 views

Computing with qutrits

I'm doing some calculations with qutrits and I need a unitary matrix $U$ that does the following: $$U|00\rangle = |12 \rangle - | 21\rangle $$ $$U|11\rangle = |20 \rangle - | 02\rangle $$ $$U|22\...
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158 views

Why can a point in anti-de Sitter space be modeled as a logical qutrit and how is its error correction done?

This isn't my area but the recent Quanta article How Space and Time Could Be a Quantum Error-Correcting Code struck me as interesting. They mention: In their paper[1] conjecturing that holographic ...
6
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1answer
484 views

Problem about qutrit teleportation protocol

I'm working through Scott Aaronson's Quantum Information Science problem sets, and I'm having trouble with a specific problem in ps5 (PDF). Specifically the following problem: A “qutrit” has the form ...
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2answers
686 views

Geometry of qutrit and Gell-Mann matrices

I need some useful sources about the geometry of qutrit. Specifically related to the Gell-Mann matrix representation.
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2answers
1k views

Difference between 3 qubits, 2 qutrits & 1 six level qunit

What is the difference between 3 qubits, 2 qutrits and a 6th level qunit? Are they equivalent? Why / why not? Can 6 classical bits be super-densely coded into each?
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284 views

Confusion regarding projection operator

Suppose we have a qutrit with the state vector $|\psi\rangle = a_0|0\rangle + a_1|1\rangle + a_2|2\rangle$, and we want to project its state onto the subspace having the basis $\{|0\rangle,|2\rangle\}$...
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2answers
435 views

Why is the decomposition of a qubit-qutrit Hamiltonian in terms of Pauli and Gell-Mann matrices not unique?

If I have the $X$ gate acting on a qubit and the $\lambda_6$ gate acting on a qutrit, where $\lambda_6$ is a Gell-Mann matrix, the system is subjected to the Hamiltonian: $\lambda_6X= \begin{pmatrix}0 ...
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533 views

Are qutrits more robust to decoherence?

A string of $n$ qutrits has a state-space spanned by the $3^n$ different states $\lvert x \rangle $ for strings $x \in \{0,1,2\}^n$ (or $x \in \{-1,0,+1\}^n$, equivalently), while $n $ qubits can ...